Branched Path Tracing
So what is "Arnold Renderer theory"? 

Let's read some Arnold documentation:


  Camera (AA) Supersampling control over the number of rays per pixel that will be traced from the camera. The higher the number of samples, the better the anti-aliasing quality, and the longer the render times. (...) This control acts as a global multiplier of all the different rays, multiplying the number of Diffuse and Glossy rays. Motion blur and depth of field quality can only be improved by increasing Camera samples.


This is also true in Cycles:



As you can see, the total number of SS samples is the number of AA samples multiplied by the number of SS samples.

How should we work with these values? As another Arnold page explains:


  Noise nearly always comes from insufficient sampling, but increasing sampling for the wrong rays can make the render times increase without helping to remove the noise. As an artist is usually working to a render time limit or amount of rays the aim is to allocate those rays as effectively as possible to minimize the noise in the most efficient manner. So if the Camera samples have to be increased to remove DOF noise, the other settings must be lowered to keep render times manageable. However, if DOF or motion blur is not a concern, then increasing Camera samples would fix all noise elsewhere but would also slow render times from the unnecessary rays.


This suggests that you have a rays budget, all rays are equally useful and expensive, and 64 AA rays with 1 diffuse ray per AA ray should be the same as 1 AA ray with 64 diffuse rays per AA ray. Let's examine this in detail. I will call the following configuration the 64*1 config:



And I will call the following the 1*64 config:



If I understand your question correctly, you expect these two configurations to create the same results equally fast, but this is not true: the 64*1 is better and slower than the 1*64: 



Is this a bug in Cycles? 

No, I actually tested it in Maya+Arnold, and there are also similar differences. The Arnold settings were the following (note that Arnold always uses "squared samples"):



OK, it is not a bug, but how do you explain the difference?

One obvious difference is that the 64*1 image is anti-aliased, while the 1*64 is not. About the rendering time also consider that the initial number of AA/camera rays does matter, those initial AA/camera rays have to be calculated, and 64 AA rays are more than 1 AA ray. And probably the code is full of tricks and optimizations that could work in one specific case, but not in another.

Conclusion: Don't take the "Arnold Renderer theory" about the "rays budget" too literally, even in Arnold it does not work exactly that way. It is not enough to think about the number of rays, it is necessary to analyze the render passes in every scene, and play with the settings until you find the optimal configuration.



It is also interesting to check the individual render passes. 

The shadow pass is very ugly in the 1*64 case, it contains only black and white, suggesting that Cycles uses only one shadow ray per AA ray.  

The diffuse indirect pass was actually better in the 1*64 setup.

The lack of AA made several 1*64 passes ugly, but for some passes the anti-aliasing was bad in the 64*1 version (and in the simple pathtracing) as well. 



As an interesting fact, I see another problem with these settings, as described here: Minimum number of samples for the Branched Path Tracing